Three sailors and two civilians were also killed in Wednesday's raids in and around the government-held town of Muttur, the defence ministry said.
In a statement, the ministry said that "during the whole incident, troops attacked the terrorists in retaliation causing them heavy casualties, killing over 40 Tiger cadres and wounding 70 other terrorists."
An artillery shell fired by the rebels hit the main hospital in Muttur, killing a civilian and a hospital worker, the statement added.
The military's claims of rebel deaths could not immediately be confirmed.
Major Upali Rajapakse, a military spokesman, said army detachments in Trincomalee came under attack on Wednesday morning from rebels using heavy weapons.
The fighting around the eastern port of Trincomalee, is the latest in a series of bloody clashes between the army and rebels in the area.
"Our troops have retaliated with mortars and artillery and successfully repelled the attacks," he said.
The Tiger leadership has not released a statement on the clashes.
Civil war fears
Diplomats and analysts increasingly fear a return to a two-decade civil war that has killed more than 65,000 people since 1983.
Scandinavian truce monitors say a 2002 ceasefire has broken down in all but name and that the foes are locked in a low intensity war. More than 800 people have died in a series of attacks and military clashes so far this year.
"This certainly looks like a war. Neither side has shown any sign of wanting to de-escalate this situation and seek peace"
On Monday, a senior rebel in the east said an army offensive meant the ceasefire was over and that the war had started. But the government says it remains committed to the ceasefire and the Tigers say they are only acting defensively.
"This certainly looks like a war," said one diplomat.
"Neither side has shown any sign of wanting to de-escalate this situation and seek peace."
Four sailors and several Tigers were killed when the rebels fired artillery and mortars at Trincomalee harbour on Tuesday as gunboats attacked a troop transport ship.
The navy said three small Sea Tiger craft were sunk and three others were damaged.
Air force jets have bombed rebel positions in the east for seven straight days.